[R] implementation of Prentice method in cch()

From: Jin Wang <jinwang25_at_gmail.com>
Date: Tue, 15 Jul 2008 19:58:07 -0400


Case cohort function cch() is in survival package. In cch(), the prentice method is implemented like this:

Prentice <- function(tenter, texit, cc, id, X, ntot,robust){

    eps <- 0.00000001
    cens <- as.numeric(cc>0) # Censorship indicators     subcoh <- as.numeric(cc<2) # Subcohort indicators
## Calculate Prentice estimate

    ent2 <- tenter
    ent2[cc==2] <- texit[cc==2]-eps
    fit1 <- coxph(Surv(ent2,texit,cens)~X,eps=eps,x=TRUE)
## Calculate Prentice estimate and variance
    nd <- sum(cens) # Number of failures

    nc <- sum(subcoh) # Number in subcohort
    ncd <- sum(cc==1) #Number of failures in subcohort
    X <- as.matrix(X)

    aent <- c(tenter[cc>0],tenter[cc<2])     aexit <- c(texit[cc>0],texit[cc<2])
    aX <- rbind(as.matrix(X[cc>0,]),as.matrix(X[cc<2,]))
    aid <- c(id[cc>0],id[cc<2])
    dum <- rep(-100,nd)
    dum <- c(dum,rep(0,nc))

    gp <- rep(1,nd)
    gp <- c(gp,rep(0,nc))
    fit <-
coxph(Surv(aent,aexit,gp)~aX+offset(dum)+cluster(aid),eps=eps,x=TRUE,
                 iter.max=35,init=fit1$coefficients)
    db <- resid(fit,type="dfbeta")

    db <- as.matrix(db)
    db <- db[gp==0,]
    fit$phase2var<-(1-(nc/ntot))*t(db)%*%(db)
    fit$naive.var <- fit$naive.var+fit$phase2var
    fit$var<-fit$naive.var

    fit$coefficients <- fit$coef <- fit1$coefficients     fit
}

The first fit1<-coxph() estimate the coefficient and second fit<-coxph() which seems a SelfPrentice method to estimate the variance. My question is why second coxph() estimate Prentice variance using SelfPrentice method. Should the jacknife variance of Prentice be implemented like: fit1 <- coxph(Surv(ent2,texit,cens)~X+cluster(id),eps=eps,x=TRUE) Th other question is unique id is not necessary in whole program, Can we just allow multiple ids without affecting the final result?

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